Dhwanil Shukla

California Institute of Technology, Pasadena, California

Ronald D. Noebe

Glenn Research Center, Cleveland, Ohio

Aaron P. Stebner

California Institute of Technology, Pasadena, California

Empirical Study of the Multiaxial, 

Thermomechanical Behavior of

NiTiHf Shape Memory Alloys

NASA/TM—2013-216619

December 2013
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Dhwanil Shukla

California Institute of Technology, Pasadena, California

Ronald D. Noebe

Glenn Research Center, Cleveland, Ohio

Aaron P. Stebner

California Institute of Technology, Pasadena, California

Empirical Study of the Multiaxial, 

Thermomechanical Behavior of

NiTiHf Shape Memory Alloys

NASA/TM—2013-216619

December 2013

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

This work was supported by the NASA FAP Aeronautical Sciences Project, Technical Discipline Lead Dale Hopkins.

Dhwanil Shukla is grateful to the SURF program at the California Institute of Technology for supporting the summer internship 

that made this work possible.

Available from

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7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

Level of Review: This material has been technically reviewed by technical management. 

This report contains preliminary fi ndings, 

subject to revision as analysis proceeds.
NASA/TM—2013-216619 1 

Empirical Study of the Multiaxial, Thermomechanical 

Behavior of NiTiHf Shape Memory Alloys 

Dhwanil Shukla 

California Institute of Technology 

Pasadena, California 91125 

Ronald D. Noebe 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Aaron P. Stebner 

California Institute of Technology 

Pasadena, California 91125 

Abstract 

An empirical study was conducted to characterize the multiaxial, thermomechanical responses of new 

high temperature NiTiHf alloys. The experimentation included loading thin walled tube Ni50.3Ti29.7Hf20

alloy samples along both proportional and nonproportional axial-torsion paths at different temperatures 

while measuring surface strains using stereo digital image correlation. A Ni50.3Ti33.7Hf16 alloy was also 

studied in tension and compression to document the effect of slightly depleting the Hf content on the 

constitutive responses of NiTiHf alloys. Samples of both alloys were made from nearly texture free 

polycrystalline material processed by hot extrusion. Analysis of the data shows that very small changes 

in composition significantly alter NiTiHf alloy properties, as the austenite finish (Af) temperature of the 

16-at.% Hf alloy was found to be ~60 °C less than the 20-at.% Hf alloy (~120 vs. 180 °C). In addition, the 

16-at.% Hf alloy exhibited smaller compressive transformation strains (2 vs. 2.5 percent). Multi-axial 

characterization of the 20-at.% Hf alloy showed that while the random polycrystal transformation strains 

in tension (4 percent) and compression (2.5 percent) are modest in comparison with binary NiTi 

(6 percent, 4 percent), the torsion performance is superior (7 vs. 4 percent shear strain width to the 

pseudoelastic plateau). 

1.0 Introduction

Shape Memory Alloys (SMAs) are novel materials that have the ability to return from a deformed 

state to a previously “memorized” shape. This ability results in two fundamental shape memory 

behaviors: (1) shape memory effect (SME) and (2) pseudoelasticity. Both behaviors occur because of the 

diffusionless, solid-state phase transformation between a high symmetry austenite phase and a low 

symmetry martensite phase. SME is exhibited when the phase transformation is induced by a change in 

temperature (martensite phase transforms to austenite on heating at a temperature beyond the austenite 

finish (Af) temperature) (Ref. 1). If a mechanical load is applied while the temperature is cycled, work 

may be performed during the transformation through the SME, as an SMA is able to recover the 

deformation imposed upon the martensite even in the presence of an applied load. Psuedoelasticity results 

from the stress-induced transformation of austenite to martensite at temperatures above the austenite 

finish temperature (Ref. 2). An SMA can be engineered to exhibit pseudoelasticity or SME at a targeted 

temperature by controlling the transformation temperatures through alloying and aging (Refs. 1 to 3). 

 
NASA/TM—2013-216619 2 

Of the various material systems capable of shape memory behaviors, polycrystalline NiTi is the most 

widely used in commercial applications and is central to a number of biomedical and industrial 

applications (Refs. 1 and 3). However, a major limitation of binary NiTi alloys is relatively low 

transformation temperatures (100 °C), which restricts the potential applications for these types of 

materials. Hf may be substituted for Ti in shape memory alloy compositions of NiTi to achieve properties 

that are not exhibited by binary NiTi alloys (Ref. 4), in particular, an elevation of the transformation 

temperatures. For the specific alloys studied in this work, the Hf substitution resulted in a moderate 

increase in transformation temperatures such that the austenite start temperatures were greater than 

100 °C. 

Previous studies characterizing the thermomechanical behavior of related NiTiHf alloys were limited, 

both in the range of compositions studied and in examination of only uniaxial loading (Refs. 5 to 9). 

Highly non-linear and anisotropic responses of NiTiHf are expected, even in randomly textured 

polycrystals, due to the phase transformation between a non-centrosymmetric martensite phase and a 

centrosymmetric austenite phase (Refs. 1 and 2). Thus, it is difficult to infer three-dimensional behavior 

of NiTiHf shape memory alloys from uniaxial tests. 

Thus, this study was aimed at characterizing the multi-axial (tension, torsion, compression, and 

combined tension-torsion and compression-torsion) response of a Ni50.3Ti29.7Hf20 alloy. Based on earlier 

studies (Refs. 5, 7 to 9), it is known that this alloy exhibits good uniaxial actuation and psuedoelastic 

properties. In addition, we investigated a slightly different Ni50.3Ti33.7Hf16 alloy in tension and 

compression to document the change in properties of this alloy system in response to small changes in Hf 

content, building on previous efforts on a Ni50.3Ti34.7Hf15 alloy (Ref. 6), which only went as far as 

characterizing basic transformation behaviors but not mechanical or functional properties. 

2.0 Experimental Procedures 

2.1 Material Description and Corresponding Sample Geometries 

The NiTiHf alloys used in this investigation were parts of two larger heats of Ni-rich NiTiHf (at.%) 

produced by Flowserve Corporation, Dayton, Ohio, by a cold-crucible vacuum induction melting process. 

In both cases, the cast ingots were vacuum homogenized at 1050 °C for 72 h, followed by extrusion at 

900 °C. Details of the two alloys and subsequent test samples are as follows. 

2.1.1 Ni50.3Ti29.7Hf20 Alloy Samples From Flowserve Heat no. 1: 

Material Composition (at.%) 

1. Nickel: 50.3 percent 

2. Hafnium: 20 percent 

3. Titanium: 29.7 percent 

Heat Treatment 

As-extruded material subsequently aged at 550 C for 3 hr. 

Sample Geometry 

Samples of this alloy were frabricated with thin walled tube gage sections, along with a hex and 

threaded stud on both ends for gripping purposes (Fig. 1). The tube geometry was chosen for multiaxial 

characterization of this alloy to allow for analysis to be carried out assuming the shear stress in the gage 

was uniform. 
NASA/TM—2013-216619 3 

Figure 1.—Ni50.3Ti29.7Hf20 alloy multiaxial sample geometry. (Dimensions are in mm.) 

Figure 2.—Ni50.3Ti33.7Hf16 alloy tension-compression sample geometry. (Dimensions are in mm.) 

2.1.2 Ni50.3Ti33.7Hf16 Alloy Samples From Flowserve Heat no. 2a

Material Composition (at.%) 

1. Nickel: 50.3 percent 

2. Hafnium: 16 percent 

3. Titanium: 33.7 percent 

Heat Treatment 

As-extruded material subsequently aged at 550 C for 3 hr. 

Sample Geometry 

The solid cylindrical dogbone tension-compression sample geometry consisted of a central gauge 

section with threaded studs on both ends for gripping purposes (Fig. 2). 

2.2 Test Setup 

2.2.1 Load Frame 

A hydraulic MTS (Material Test System) 3.3 kip (15 kN) axial-axis, 1300 lbf-in. (150 N-m) torsionaxis load frame was used to apply axial and torsional stress to the samples. Custom high-temperature 

capable water-cooled Inconel grips were used for holding the sample. Figure 3 shows the MTS load frame 

with the Inconel grips installed. 

2.2.2 Furnace and Temperature Control 

A 10 kW induction furnace (Fig. 4) with remote work-head and a custom-wound copper induction 

coil was used to control the sample thermal loading during testing. Other instrumentation used in thermal 

control included the water circulation unit (Fig. 5) for pumping chilled water to the induction coil and 

Inconel grips and the temperature controller (Fig. 6). Type K thermocouples were used for measuring the 

sample surface temperature. 
NASA/TM—2013-216619 4 

Figure 3.—MTS load frame with Inconel grips. 

 

Figure 4.—Induction furnace and controller. 

Figure 5.—Water circulation system. Figure 6.—Temperature controller. 
NASA/TM—2013-216619 5 

Figure 7.—Laser extensometer. Figure 8.—Components of the DIC system. 

2.2.3 Laser Extensometer 

A laser extensometer (Fig. 7) was used for non-contact measurement of strains in the Ni50.3Ti33.7Hf16

alloy samples during uniaxial testing. 

2.2.4 Digital Image Correlation System (DIC) 

The surface displacements of the Ni50.3Ti29.7Hf20 alloy samples were measured using DIC. Images of 

a painted pattern on the surface of the samples were acquired from two cameras located slightly separated 

from each other in space (binocular for 3D information capture). These photographs were then processed 

by image processing software, which tracks the movement of each speckle through the series of images 

providing the displacement of each speckle. This displacement data is then used to determine surface 

strains. The components of our DIC system include the following (Fig. 8): 

1. Two Cameras with lenses—for binocular images 

2. Camera stand—for keeping cameras stable and in position 

3. Lamp—for providing adequate high-intensity lighting for taking pictures 

4. DAQ (National Instruments)—for relaying signals from other sensors and devices 

5. PC with 3D correlation software—for performing image processing to determine displacements 

and strains 

2.3 Loading Program Segment Types 

The Type I to VII loading program segments described below were conducted only on the 

Ni50.3Ti29.7Hf20 alloy samples while the Type A, B, and C loading program segments were conducted only 

on the Ni50.3Ti33.7Hf16 alloy samples. 
NASA/TM—2013-216619 6 

2.3.1 Ni50.3Ti29.7Hf20 Alloy Samples 

Unique proportional and non-proportional mechanical loading paths were imposed upon the tubular 

specimens. We have defined the types of loading paths used in the experiments as follows, with graphical 

depictions shown in Figure 9. 

Type I: Proportional Tension:

a. Load in tension to a predetermined force linearly in force control. 

b. Unload tension back to zero force linearly in force control. 

Type II: Proportional Compression:

a. Load in compression to a predetermined force linearly in force control. 

b. Unload compression back to zero force linearly in force control. 

Type III: Proportional Torsion:

a. Load in torsion to a predetermined rotation angle linearly in rotation control. 

b. Unload torsion back to zero angle linearly in rotation control. 

Type IV: Non-Proportional Axial-Torsion (ATTA):

a. Load in Axial direction to a particular displacement linearly in displacement control. 

b. Load in Torsion to a particular rotation angle linearly in rotation control. 

c. Unload Torsion back to zero angle linearly in rotation control. 

d. Unload Axially back to zero displacement linearly in displacement control. 

Type V: Non-Proportional Axial-Torsion (ATAT):

a. Load in Axial direction to a particular displacement linearly in displacement control. 

b. Load in Torsion to a particular rotation angle linearly in rotation control. 

c. Unload Axially back to zero displacement linearly in displacement control. 

d. Unload Torsion back to zero angle linearly in rotation control. 

Thus, the loading programs of Type IV and V have the same loading paths (a, b) but different unloading 

paths (c, d). 

Type VI: Proportional Axial-Torsion (AT)(AT):

a. Load in Axial and Torsional direction simultaneously to a predetermined displacement and 

rotation in simultaneous displacement and rotation control. 

b. Unload in Axial and Torsional direction to zero displacement and angle in simultaneous 

displacement and rotation control. 

Type VII: Fixed Crosshead Thermal Cycling:

a. Changing temperature while keeping crossheads locked (fixed in displacement and rotation). 

 
NASA/TM—2013-216619 7 

Figure 9.—Graphical representations of the loading programs used to test the Ni50.3Ti29.7Hf20 alloy samples. AxialForce(F)

Time

Type I and II Loading sequence

RotationAngle()

Time

Type III Loading sequence

Displacemet/Angle

Time

Type IV Loading sequence (ATTA)

AxialDisplacement

RotationAngle

Displacement/Angle

Time

Type V Loading sequence (ATAT)

AxialDisplacement

RotationAngle

Displacement/Angle

Time

Type VI Loading sequence 

(AT)(AT)

AxialDisplacement

RotationAngle
NASA/TM—2013-216619 8 

2.3.2 Ni50.3Ti29.7Hf16 Alloy Samples 

Type A: Constant Force Thermal Cycling:

a. Load in tension or compression to a particular force. 

b. Heat sample to a specific temperature linearly at some specific rate keeping the applied force 

constant. 

c. Cool sample by switching off furnace keeping force constant. 

Type B: Constant Temperature Mechanical Cycling: 

a. Heat and maintain sample at predetermined temperature. 

b. Load in tension/compression to a particular force linearly keeping temperature constant. 

c. Unload to zero force linearly with same rate keeping temperature constant. 

Type C: Blocking Stress Test:

a. Load the sample to particular displacement value. 

b. Heat sample to a particular temperature linearly with time keeping displacement constant. 

c. Cool back to room temperature keeping displacement constant. 

2.4 Complete Test Sequences for the Ni50.3Ti29.7Hf20 Samples 

Testing was conducted on four samples. Sample 1 was loaded in compression at 180 C with fixed 0

rotation to a force of –9 kN and then unloaded. Sample 2 was loaded in tension at 180 C with fixed 0

rotation until fracture occurred in the grips. Sample 3 was subjected to a sequence of tension—torsion 

steps defined in Section 2.4.1 and Sample 4 was subjected to a sequence of compression—torsion steps 

defined in Section 2.4.2. The complete loading histories of Samples 3 and 4 follow. 

2.4.1 Sample 3—Tension-Torsion 

1. 0 N axial force, 0 rotation control, temperature cycled between 250 C and room temperature 

twice 

2. 0 N axial force, 0 rotation control, temperature increased to 180 C 

3. Type I loading: load to 4950 N (~0.8 GPa) axial force, 0 rotation control, while temperature 

maintained at 180 C 

4. Type III loading: 0 N axial force, twist to 90 rotation angle, temperature maintained at 180 C 

5. Type IV loading: load to axial displacement corresponding to ~2 percent axial strain, twist to 90

rotation angle, temperature maintained at 180 C 

6. Type V loading: load to axial displacement corresponding to ~2 percent axial strain, twist to 90

rotation angle, temperature maintained at 180 C 

7. Type VI loading: load to axial displacement corresponding to ~2 percent axial strain, twist to 90

rotation angle, temperature maintained at 180 C 

8. Type VII loading: displacement fixed, rotation angle fixed, temperature cycled between 250 C 

and room temperature twice 

9. Type VII loading: displacement fixed, rotation angle fixed, heat to 220 C 

10. Type I loading: load to 4950 N (~0.8 GPa) axial force, 0 rotation control, while temperature 

maintained at 220 C 

11. Type III loading: 0 N axial force, twist to 90 rotation angle, temperature maintained at 220 C 

12. Type VI loading: load to axial displacement corresponding to ~2 percent axial strain, twist to 90

rotation angle, temperature maintained at 220 C 

13. Type IV loading: load to axial displacement corresponding to ~2 percent axial strain, twist to 90

rotation angle, temperature maintained at 220 C 

14. Type V loading: load to axial displacement corresponding to ~2 percent axial strain, twist to 90

rotation angle, temperature maintained at 220 C 
NASA/TM—2013-216619 9

15. Unload axial and torsional stresses, while maintaining temperature at 220 C

16. 0 N axial force, 0 N-m torque, decrease temperature to RT

17. Unload

2.4.2 Sample 4—Compression-Torsion 

1. 0 N axial force, 0 rotation control, temperature cycled between 250 C and room temperature

twice

2. 0 N axial force, 0 rotation control, temperature increase to 180 C

3. Type II loading: load to –4950 N (~–0.8 GPa) axial force, 0 rotation control, temperature

maintained at 180 C

4. Type III loading: 0 N axial force, twist to 90 rotation angle, temperature maintained at 180 C

5. Type IV loading: load to axial displacement corresponding to ~–2 percent axial strain, twist to 90

rotation angle, temperature maintained at 180 C

6. Type V loading: load to axial displacement corresponding to ~–2 percent axial strain, twist to 90

rotation angle, temperature maintained at 180 C

7. Type VI loading: load to axial displacement corresponding to ~–2 percent axial strain, twist to 90

rotation angle, temperature maintained at 180 C

8. Type VII loading: displacement fixed, rotation angle fixed, temperature cycled between 250 C

and room temperature twice

9. Type VII loading: displacement fixed, rotation angle fixed, heat to 220 C

10. Type II loading: load to –4950 N (~–0.8 GPa) axial force, 0 rotation control, temperature

maintained at 220 C

11. Type III loading: 0 N axial force, twist to 90 rotation angle, temperature maintained at 220 C

12. Type VI loading: load to axial displacement corresponding to ~–2 percent axial strain, twist to 90

rotation angle, temperature maintained at 220 C

13. Type V loading: load to axial displacement corresponding to ~–2 percent axial strain, twist to 90

rotation angle, temperature maintained at 220 C

14. Type IV loading: load to axial displacement corresponding to ~–2 percent axial strain, twist to 90

rotation angle, temperature maintained at 220 C

15. Unload axial and torsional stresses, while maintaining temperature at 220 C

16. 0 N axial force, 0 N-m torque, decrease temperature to RT

17. Unload

2.5 Complete Test Sequences for the Ni50.3Ti33.7Hf16 Samples 

A total of seven samples were used to characterize the tension-compression behavior of the 16-at.% 

Hf alloy. Their loading histories follow. 

2.5.1 Sample 1 

1. Type A loading: –159 N (–10 MPa), 0 to 240 C, two thermal cycles

2. Type A loading: –1587 N (–100 MPa), 0 to 240 C, two thermal cycles

3. Type A loading: –3175 N (–200 MPa), 0 to 240 C, two thermal cycles

4. Type A loading: –6350 N (–400MPa), 0 to 240 C, two thermal cycles

5. Type A loading: 1587 N (100 MPa), 0 to 240 C, two thermal cycles

6. Type A loading: 3175 N (200 MPa), 0 to 240 C, two thermal cycles

7. The sample failed in the threads while loading to 6350 N (400 MPa)
NASA/TM—2013-216619 10

2.5.2 Sample 2 

1. Type B loading: 160 C, –16740 N

2. Type B loading: 160 C, –3736 N

3. Type B loading: 160 C, –5990 N

4. Type B loading: 160 C, –12000 N

5. Type B loading: 160 C, –13000 N

6. Type B loading: 150 C, –13000 N

7. Type B loading: 150 C, –13000 N

8. Type B loading: 25 C, –12000 N

9. Type B loading: 25 C, –13000 N

10. Type A loading: –7729 N (–600 MPa), 0 to 240 C, two thermal cycles

11. Type A loading: –10305 N (–800 MPa), 0 to 240 C, two thermal cycles

12. Type A loading: –12882 N (–1000 MPa), 0 to 240 C, two thermal cycles

2.5.3 Sample 3 

1. Type A loading: –1288 N (–100 MPa), 0 to 240 C, two thermal cycles

2. Type A loading: –2576 N (–200 MPa), 0 to 240 C, two thermal cycles

3. Type A loading: –5153 N (–400 MPa), 0 to 240 C, two thermal cycles

4. Type A loading: –7729 N (–600 MPa), 0 to 240, C, two thermal cycles

5. Type A loading: –10306 N (–800 MPa), 0 to 240 C, two thermal cycles

6. Type A loading: –12882 N (–1000 MPa), 0 to 240 C, two thermal cycles

7. Type A loading: 0 MPa, 0 to 240 C, two thermal cycles

8. Type B loading: 25 C, –7729 N

9. Type A loading: 0 MPa, 0 to 240 C, one thermal cycle

10. Type B loading: 25 C, –10306 N

11. Type A loading: 0 MPa, 0 to 240 C, one thermal cycle

12. Type B loading: 25 C, –12882 N

13. Type A loading: 0 MPa, 0 to 240 C, one thermal cycle

2.5.4 Sample 4 

1. Type B loading: 25 C, 7729 N

2. Type A loading: 0 MPa, 0 to 240 C, one thermal cycle

3. Type B loading: 25 C, 10306 N

4. Type A loading: 0 MPa, 0 to 240 C, one thermal cycle

5. Type B loading: 25 C, 10306 N

6. Type A loading: 0 N, 0 to 240 C, one thermal cycle

7. Type B loading: 25 C, –12882 N

8. Type A loading: 0 N, 0 to 240 C one thermal cycle

2.5.5 Sample 5 

1. Type A loading: 0 N, 0 to 240 C, two thermal cycles

2. Type B loading: 25 C, 7729 N

3. Type A loading: 0 N, 0 to 240 C, one thermal cycle

4. Type B loading: 25 C, 10306 N

5. Type A loading: 0 N, 0 to 240 C, one thermal cycle

6. Type B loading: 25 C, 10306 N

7. Type A loading: 0 N, 0 to 240 C, one thermal cycle
NASA/TM—2013-216619 11

8. Type B loading: 25 C, –12882 N

9. Type A loading: 0 N, 0 to 240 C, one thermal cycle

2.5.6 Sample 6 

1. Type A loading: 0 N, 0 to 240 C, two thermal cycles

2. Type C loading: displacement corresponding to ~–1 percent strain, 0 to 240 C, two thermal

cycles

3. Type C loading: displacement corresponding to ~–2.5 percent strain, 0 to 240 C, two thermal

cycles

2.5.7 Sample 7 

1. Type A loading: 0 N, 0 to 240 C, two thermal cycles

2. Type C loading: displacement corresponding to ~–0.5 percent strain, 0 to 240 C, two thermal

cycles

3. Unload sample in stress

4. Type A loading: 0 N, 0 to 240 C, two thermal cycles

5. Type B loading: 25 C, 5153 N

6. Type A loading: 0 N, 0 to 240 C, two thermal cycles

7. Sample failed in threads at 558 MPa (1788 N) while trying to do Type B loading at 25 C to

600 MPa (7729 N)

Note that throughout the test sequences above the step ‘Type A loading: 0 N, 0 to 240 C two thermal 

cycles’ has been used for resetting the material into a stress-free state. 

3.0 Results 

The results of the experiments conducted in this study are primarily presented as plots of engineering 

equivalent stress and engineering equivalent strains. However, some plots are just engineering stress 

versus engineering strain plots. The equivalent stresses and strains are obtained by the expressions: 





 



	


  
  
 
  
  
 2 2 2 2

3

4

eq a 3 t and eq a t (1)

respectively, where 


eq = Equivalent Engineering Stress 


a = Axial Engineering Stress 


t = Torsional Engineering Stress 


eq = Equivalent Engineering Strain 


a = Axial Engineering Strain 


t = Torsional Engineering Strain 
NASA/TM—2013-216619 12 

3.1 Ni50.3Ti29.7Hf20 Alloy Experimental Data

Note that the Type I to VII loading programs were conducted on the Ni50.3Ti29.7Hf20 alloy samples 

only, while Type A, B, and C loading programs were conducted only on the Ni50.3Ti33.7Hf16 alloy samples. 

The experimental results for the Ni50.3Ti29.7Hf20 alloy samples are presented below in the same order as 

described in Section 2.4. Subsequent to inserting the samples into the grips, but prior to all deformations 

reported in this work, specimens were heated and cooled twice between room temperature and 240 C in 

0 load, 0 torque control. Nothing other than normal thermal expansion was observed, so these data are not 

reported. For each of the four samples, the complete data set for each load segment are reported in 6 

subplots: (a) stress-strain, where axial, torsion, and Mises mechanical responses are shown; (b) effective 

axial versus torsion strain; (c) effective axial versus torsion stress; (d) axial force and displacement versus 

time; (e) torque and rotation versus time; and (f) standard deviation of the axial and shear strain 

calculations from the DIC analysis versus time. 

3.1.1 Sample 1 

The motivation for this test was to begin to test the limit of compression loading on the tube 

geometry. As the results in Figure 10 demonstrate, the sample geometry could be loaded successfully to 

1.5 GPa in compression without any buckling. 

Figure 10.—Ni50.3Ti29.7Hf20 Sample 1 responses. 
NASA/TM—2013-216619 13

3.1.2 Sample 2 

The data in Figure 11 was obtained while attempting to run to 1.5 GPa in tension. The sample broke 

in the grip at the threads at about 1 GPa. Therefore, subsequent tests were restricted to loading to 0.8 GPa 

in tension to prevent failure of additional samples. 

Figure 11.—Ni50.3Ti29.7Hf20 Sample 2 responses. 
NASA/TM—2013-216619 14 

3.1.3 Sample 3 

This sample was utilized in performing a series of Tension-Torsion loading experiments at 180 and 

220 C. Refer to Section 2.4.1 for a complete loading history for the sample and for additional details of 

the various test sequence segments. 

3.1.3.1 Type I Loading at 180 C 

Some slipping of the threads in the grips was observed during this test and resulted in the “steps” 

observed in the stress-strain curve. Adjustments were made to subsequent samples and the mechanical 

contact seemed to stabilize in subsequent tests. 

Figure 12.—Ni50.3Ti29.7Hf20 Sample 3 responses for test sequence segment no. 3. Type I loading 

to 4950 N (~0.8 GPa) axial force, 0 rotation control, and temperature maintained at 180 C.

 
NASA/TM—2013-216619 15 

3.1.3.2 Type III Loading at 180 C 

This data was recorded after three unsuccessful trials due to a grip holder nut that kept breaking loose. 

Some substantial torque was applied during the failed trials but stress was well below the plastic flow 

stress. In this test, a bit of slipping of the nut around 6 N-m load was also observed, but it tightened after 

that for the remainder of the tests. The steps in the stress-strain curve (increase in torque without increase 

in strain) are from this slippage in the grips and is not a material response. 

Figure 13.—Ni50.3Ti29.7Hf20 Sample 3 responses for test sequence segment no. 4. Type III loading with 

0 N axial force, twist to 90 rotation angle, temperature maintained at 180 C. 

 
NASA/TM—2013-216619 16

3.1.3.3 Type IV Loading at 180 C 

Figure 14.—Ni50.3Ti29.7Hf20 Sample 3 responses for test sequence segment no. 5. Type IV loading to an axial 

displacement corresponding to ~2 percent axial strain, twist to 90 rotation angle, while temperature was 

maintained at 180 C.
NASA/TM—2013-216619 17 

3.1.3.4 Type V Loading at 180 C 

Figure 15.—Ni50.3Ti29.7Hf20 Sample 3 responses for test sequence segment no. 6. Type V 

loading to an axial displacement corresponding to ~2 percent axial strain, twist to 90

rotation angle, while temperature was maintained at 180 C.

 
NASA/TM—2013-216619 18 

3.1.3.5 Type VI Loading at 180 C 

Figure 16.—Ni50.3Ti29.7Hf20 Sample 3 responses for test sequence segment no. 7. Type VI 

loading to an axial displacement corresponding to ~2 percent axial strain, twist to 90

rotation angle, while temperature was maintained at 180 C. 

 
NASA/TM—2013-216619 19

3.1.3.6 Type I Loading at 220 C 

Before this test segment, the sample was cycled in temperature between 240 C and RT twice and 

then heated to 220 C with crossheads fixed (in both axial and rotation). See Section 2.4.1 for details. 

Figure 17.—Ni50.3Ti29.7Hf20 Sample 3 responses for test sequence segment no. 10. Type I loading to 

4950 N (~0.8 GPa) axial force, 0 rotation control, while temperature maintained at 220 C.
NASA/TM—2013-216619 20

3.1.3.7 Type III Loading at 220 C 

Figure 18.—Ni50.3Ti29.7Hf20 Sample 3 responses for test sequence segment no. 11. Type III loading 

with 0 N axial force, twist to 90 rotation angle, while temperature was maintained at 220 C. 
NASA/TM—2013-216619 21

3.1.3.8 Type VI Loading at 220 C 

Figure 19.—Ni50.3Ti29.7Hf20 Sample 3 responses for test sequence segment no. 12. Type VI 

loading to an axial displacement corresponding to ~2 percent axial strain, twist to 90

rotation angle, while temperature maintained at 220 C.
NASA/TM—2013-216619 22

3.1.3.9 Type IV Loading at 220 C 

Figure 20.—Ni50.3Ti29.7Hf20 Sample 3 responses for test sequence segment no. 13. 

Type IV loading to an axial displacement corresponding to ~2 percent axial strain, 

twist to 90 rotation angle, while temperature maintained at 220 C.
NASA/TM—2013-216619 23

3.1.3.10 Type V Loading at 220 C 

Figure 21.—Ni50.3Ti29.7Hf20 Sample 3 responses for test sequence segment no. 14. Type V loading to 

an axial displacement corresponding to ~2 percent axial strain, twist to 90 rotation angle, while 

temperature maintained at 220 C.
NASA/TM—2013-216619 24 

3.1.4 Sample 4 

This sample was utilized in performing a series of Compression-Torsion experiments at 180 and 220 

C. Refer to Section 2.4.2 for a complete loading history for the sample and for additional details of the 

various test sequence segments. 

3.1.4.1 Type II Loading at 180 C 

Figure 22.—Ni50.3Ti29.7Hf20 Sample 4 responses for test sequence segment no. 3. Type II loading to 

–4950 N (~–0.8 GPa) axial force, 0 rotation control, while temperature maintained at 180 C.

 
NASA/TM—2013-216619 25 

3.1.4.2 Type III Loading at 180 C 

This data was recorded after 2 unsuccessful trials due to a grip holder nut breaking loose. Some 

substantial torque was applied during the failed trials but plastic strain data could not be recorded. 

However, it was assumed that there were no plastic strains imparted to the sample during the failed trials. 

 

Figure 23.—Ni50.3Ti29.7Hf20 Sample 4 responses for test sequence segment no. 4. Type III loading at 0 N axial 

force, twist to 90 rotation angle, while temperature maintained at 180 C. 
NASA/TM—2013-216619 26 

3.1.4.3 Type IV Loading at 180 C 

The initial stress observed in the plots is due to torque introduced to tighten the nut, which broke 

loose while performing the first attempt at this segment. This residual torque is carried through the 

remainder of the test segments for this sample. 

Figure 24.—Ni50.3Ti29.7Hf20 Sample 4 responses for test sequence segment no. 5. Type IV loading to 

an axial displacement corresponding to ~–2 percent axial strain, twist to 90 rotation angle, while 

temperature maintained at 180 C. 

 
NASA/TM—2013-216619 27 

3.1.4.4 Type V Loading at 180 C 

Figure 25.—Ni50.3Ti29.7Hf20 Sample 4 responses for test sequence segment no. 6. Type V 

loading to an axial displacement corresponding to ~–2 percent axial strain, twist to 90

rotation angle, while temperature maintained at 180 C. 

 
NASA/TM—2013-216619 28 

3.1.4.5 Type VI Loading at 180 C 

Figure 26.—Ni50.3Ti29.7Hf20 Sample 4 responses for test sequence segment no. 7. Type VI 

loading to an axial displacement corresponding to ~–2 percent axial strain, twist to 90

rotation angle, while temperature maintained at 180 C. 

 
NASA/TM—2013-216619 29 

3.1.4.6 Type II Loading at 220 C 

Before this test, the sample was cycled in temperature between 240 C and RT twice and then heated 

to 220 C with crossheads fixed (in both axial and rotation). For a complete history of the loading 

sequence segments on this sample, see Section 2.4.2. 

Figure 27.—Ni50.3Ti29.7Hf20 Sample 4 responses for test sequence segment no. 10. Type II loading 

to –4950 N (~–0.8 GPa) axial force, 0 rotation control, while temperature maintained at 220 C.
NASA/TM—2013-216619 30 

3.1.4.7 Type III Loading at 220 C 

Figure 28.—Ni50.3Ti29.7Hf20 Sample 4 responses for test sequence segment no. 11. Type III 

loading at 0 N axial force, twist to 90 rotation angle, while temperature maintained at 220 C. 

 
NASA/TM—2013-216619 31 

3.1.4.8 Type VI Loading at 220 C 

Figure 29.—Ni50.3Ti29.7Hf20 Sample 4 responses for test sequence segment no. 12. Type VI 

loading to an axial displacement corresponding to ~–2 percent axial strain, twist to 90

rotation angle, while temperature maintained at 220 C.

 
NASA/TM—2013-216619 32 

3.1.4.9 Type V Loading at 220 C 

Figure 30.—Ni50.3Ti29.7Hf20 Sample 4 responses for test sequence segment no. 13. Type V 

loading to an axial displacement corresponding to ~–2 percent axial strain, twist to 90

rotation angle, while temperature maintained at 220 C.

 
NASA/TM—2013-216619 33 

3.1.4.10 Type IV Loading at 220 C 

Figure 31.—Ni50.3Ti29.7Hf20 Sample 4 responses for test sequence segment no. 14. Type IV loading to 

an axial displacement corresponding to ~–2 percent axial strain, twist to 90 rotation angle, while 

temperature maintained at 220 C.

 
NASA/TM—2013-216619 34 

3.2 Ni50.3Ti33.7Hf16 Alloy Experimental Data 

The experimental results for the Ni50.3Ti33.7Hf16 alloy samples are grouped and presented in the order 

of the loading types described in Section 2.3.2 in the subsections that follow. 

3.2.1 Type A Loading 

Type A loading segments (defined in Section 2.3.3) were performed on Samples 1, 2, and 3 (the 

complete test history for each sample is described in Section 2.5). Figure 32 includes plots of Type A 

loading tests on Sample 1. The plots for –200, –400, 100, and 200 MPa are shifted in strain because the 

extensometer was disturbed after the –100 MPa thermal cycle. Thus, these plots can be used to refer 

quantitatively only to determination of the phase transformation temperatures. Data for Samples 2 and 3 

are contained in Figures 33 and 34, respectively, while comparisons of the isobaric thermomechanical 

response of Samples 2 and 3 are shown in Figures 35 to 37. 

Figure 32.—Thermomechanical responses of Ni50.3Ti33.7Hf16 alloy 

Sample 1 when subjected to Type A loading segments. 

Figure 33.—Thermomechanical responses of Ni50.3Ti33.7Hf16 alloy Sample 2 

when subjected to Type A loading segments. 
NASA/TM—2013-216619 35 

Figure 34.—Thermomechanical responses of Ni50.3Ti33.7Hf16 alloy Sample 3 when 

subjected to Type A loading segments over a broad range of compressive stress. 

Figure 35.—Comparison of the responses of Ni50.3Ti33.7Hf16 alloy Samples 2 and 3 

subjected to Type A loading to –7729 N force (–600 MPa) for determining reproducibility 

of the test results and stability and history dependence of the material to various loading 

programs. 
NASA/TM—2013-216619 36 

Figure 36.—Comparison of responses of Ni50.3Ti33.7Hf16 alloy Samples 2 and 3 subjected 

to Type A loading to –10306 N force (–800 MPa) for determining reproducibility of the 

test results and stability and history dependence of the material to various loading 

programs. 

Figure 37.—Comparison of responses of Ni50.3Ti33.7Hf16 alloy Samples 2 and 3 subjected 

to Type A loading to –12882 N force (–1000 MPa) for determining reproducibility of the 

test results and stability and history dependence of the material to various loading 

programs. 

 
NASA/TM—2013-216619 37 

3.2.2 Type B Loading 

Type B loading segments were performed on Samples 2, 3, 4, 5, and 7. In Figure 38, the strain is 

proportional to stress at temperatures of 150 and 160 C indicating that the yield strength for the material 

is above 1 GPa at these temperatures and also indicating that there is no phase transformation (from 

austenite to martensite) at least for stresses below 1 GPa. It is possible that at these temperatures, the 

stress-induced transformation could still occur at higher stress levels, assuming that plastic deformation 

does not occur first. The tests at room temperature were performed without any prior thermal cycling at 

zero stress (for resetting the alloy). Hence, the curve for the 13000 N force test starts very near the end of 

the curve for the 12000 N force test, which was performed immediately before it. The legend sequence in 

Figure 38 appears in the same order as the actual loading sequence for this sample. 

Figure 39 shows Type B loading segments on Sample 3 at –600, –800 and –1000 MPa. The tests were 

performed after completing Type A loading segments (as shown in Fig. 34). A complete loading history 

for Sample 3 is described in Section 2.5.3. The curve corresponding to –600 MPa load starts from a strain 

value different from the plots corresponding to –800 and –1000 MPa because the sample had a history of 

strain, which was reset (heating to 240 C and back to room temperature at 0 MPa stress) after the loading 

sequence to –600 and –800 MPa. 

Figure 38.—Stress-strain responses of Ni50.3Ti33.7Hf16 alloy Sample 2 subjected to 

Type B loading segments. 

Figure 39.—Stress-strain responses of Ni50.3Ti33.7Hf16 alloy Sample 3 subjected to 

Type B loading segments. 
NASA/TM—2013-216619 38 

Figure 40 shows Type B loading segments on a virgin, as-received sample (Sample 4), which did not 

have any thermomechanical cycles prior to testing. The plot for –600 MPa starts at 0 strain but recovers to 

a different strain value after unloading and stress free thermal cycling. This is presumably due to residual 

strain introduced during processing and machining of the original material. To check if this was the case, 

Sample 5 was also loaded similarly, with the only difference that it was temperature cycled to 240 C and 

back at 0 MPa twice before loading to –600 MPa. The results (Fig. 41) seem to confirm that the offset 

observed in the case of Sample 4 was due to residual stress in the as-processed sample. 

Figure 40.—Stress-strain responses of Ni50.3Ti33.7Hf16 alloy Sample 4 subjected to 

Type B loading segments. 

Figure 41.—Stress-strain responses of Ni50.3Ti33.7Hf16 alloy Sample 2 subjected to 

Type B loading segments. 
NASA/TM—2013-216619 39 

Figures 42 to 44 provide a measure of the reproducibility of the test data at a particular stress level, 

given the large difference in loading history for each sample. Data for Samples 4 and 5 were more 

consistent than that for Sample 3, which underwent a significant number of Type A loading events prior 

to the isothermal deformations (Type B loading). 

Figure 42.—Comparison of the responses for Ni50.3Ti33.7Hf16 alloy Samples 3 to 5 

subjected to Type B loading to –7729 N force (–600 MPa) for determination of the 

reproducibility of the test data and stability of the material (initial strains adjusted to 

zero). 

Figure 43.—Comparison of the responses of Ni50.3Ti33.7Hf16 alloy Samples 3 to 5 subjected 

to Type B loading to –10306 N force (–800 MPa) for determination of the reproducibility 

of the test data and stability of the material (initial strains adjusted to zero). 
NASA/TM—2013-216619 40 

Figure 44.—Comparison of the responses of Ni50.3Ti33.7Hf16 alloy Samples 3 to 5 

subjected to Type B loading to –12882 N force (–1000 MPa) for determination of the 

reproducibility of the test data and stability of the material (initial strains adjusted to 

zero). 

Figure 45.—Stress-strain responses of Ni50.3Ti33.7Hf16 alloy Sample 7 subjected to 

Type B loading to 400 MPa. 

Figure 45 is plot of a Type B loading test performed in tension at 400 MPa on Sample 7. The sample 

subsequently failed in the threads during the next cycle while loading to 600 MPa (Fig. 46). 

Consequently, the number of tension tests in the study was limited because of the tendency for the 

Ni50.3Ti33.7Hf16 alloy to fail in the threads during tensile loading at stresses near 500 MPa. 

 
NASA/TM—2013-216619 41 

Figure 46.—Stress-strain response of Ni50.3Ti33.7Hf16 alloy Sample 7 to failure while 

loaded in tension. 

Figure 47.—Stress-temperature responses of Ni50.3Ti33.7Hf16 alloy Sample 6 subjected to 

Type C loadings. 

3.2.3 Type C Loading 

Type C loading was performed on Samples 6 and 7. Figure 47 is the result obtained for a blocking 

experiment (Type C loading) performed on Sample 6 constrained at ~–1 percent strain during thermal 

cycling. Figure 48 is the result obtained for a similar blocking experiment performed on Sample 6 but 

constrained at ~–2.5 percent strain. During this experiment the axial force exceeded 13000 N (in 

compression) while temperature cycling, while the load frame’s limit was 13000 N. Hence the load frame 

could not keep the crosshead fixed during the experiment and the blocking experiment could not be 

performed as required. The variation of strain with temperature is plotted in Figure 49 (which should have 

been a straight horizontal line if the limit of the test frame had not been exceeded) to show how much the 

test deviated from the desired limit. However, this result does indicate that very significant stresses are 

generated during the thermally induced martensite-to-austenite transformation in this material. Figure 50 

is the result obtained for Type C loading (blocking experiment) performed on Sample 7 constrained at a 

much more modest ~–0.5 percent strain. 
NASA/TM—2013-216619 42 

Figure 48.—Stress-temperature responses of Ni50.3Ti33.7Hf16 alloy Sample 6 subjected to 

Type C loadings. 

Figure 49.—Variation in strain while attempting to perform Type C loading on 

Ni50.3Ti33.7Hf16 alloy Sample 6 as the load limit of the test frame was exceeded. 
NASA/TM—2013-216619 43 

Figure 50.—Stress-temperature responses of Ni50.3Ti33.7Hf16 alloy Sample 7 subjected to 

Type C loadings. 

4.0 Discussion of Important Observations 

Results from the Type I (proportional tension), shown in Figures 12 and 17, and Type II (proportional 

compression), shown in Figures 22 and 27, loading routines on the Ni50.3Ti29.7Hf20 alloy, indicate that 

the transformation stress for the material is higher at 220 C than at 180 C. This suggests that for the 

Ni50.3Ti29.7Hf20 alloy the stress-induced phase transformation from austenite to martensite occurs more 

easily at lower temperatures (within a temperature range above Af) as stability of the austenite phase 

increases with temperature. This is consistent with the established understanding of the stress-temperature 

dependence of the martensitic transformation via the Clausius-Clapeyron relationship as applied to SMAs 

(Refs. 7 and 10). However, the fact that the stress-induced transformation for this alloy occurs at such 

high temperatures and in a stable manner, as previously confirmed in similar materials (Refs. 5, 7, and 8), 

is a significant advantage over binary NiTi alloys. 

Figures 32 to 34 provide an indication of the phase transformation temperatures for the Ni50.3Ti33.7Hf16

alloy as a function of applied stress. In particular, the phase transformation temperatures observed for the 

16-at.% Hf alloy are ~60 C less than those observed from Type A testing of previous Ni50.3Ti29.7Hf20

alloys (Refs. 5, 7, and 9). Thus the effect of Hf concentration on phase transformation temperatures is 

apparent: an increase in Hf content leads to an increase in transformation temperatures. This is also 

consistent with the findings of Potapov et al. (Ref. 11). 

What is much more interesting, is that the results indicate that increasing Hf content leads to an 

increase in tension and compression transformation strains, when comparing the results of the 16-at.% Hf 

alloy with the 20-at.% Hf results of Bigelow et al. (Ref. 5) and Benafan et al. (Ref. 9). For example, the 

16-at.% Hf alloy exhibited ~1.5 percent tension, 1.25 percent compression transformation strains under 

200 MPa load whereas the 20-at.% Hf alloy exhibited ~2.75 percent tension, 1.75 percent compression 

transformation strains under the same isobaric conditions (Ref. 5). The trend is also consistent for 

transformation strains under other loads. The 16-at.% Hf alloy, however, shows no signs of plastic 

deformation, or “open loop” strain under 1 GPa compressive loads (Fig. 33), while in unpublished 

research, Bigelow et al. have shown that the 20-at.% Hf alloy begins to exhibit open loop strain at loads 

of 800 MPa. This finding suggests that the 16-at.% Hf alloy is stronger. 

In fact, we found that the macroscopic yield stress of the Ni50.3Ti33.7Hf16 alloy is ~1600 MPa effective 

stress, independent of loading mode (Figs. 13, 23 to 26, and 28 to 31). This is significantly larger than the 

strength of binary NiTi, which ranges from 600 to 1200 MPa (Refs. 1 and 10). However, consistent with 

the Bigelow et al. result, we also observed the development of unrecovered strains due to plasticitytransformation interactions when the material was loaded in excess of 800 MPa but below the 1600 MPa 
NASA/TM—2013-216619 44 

effective stress (Figs. 14 to 16 and 19 to 21) as the applied strain was not fully recovered during these 

loading sequences.

The other important observation is made from the plots in Figures 10, 11, and 13. The ‘plateau’ in the 

case of tension only, compression only, and torsion only loading of the Ni50.3Ti29.7Hf20 alloy start at 

different equivalent stress values (noting that the equivalent stress—strain curve is essentially the same as 

an axial stress strain curve for Type I and II loading). Also, the transformation strains in all three types of 

loadings are different, the largest being the case of torsional loading. This suggests that the material is 

highly asymmetric. Also, the larger torsion transformation strain (7 percent shear strain width to the 

pseudoelastic plateau) than binary NiTi (~4 percent shear strain width to the pseudoelastic plateau 

(Ref. 12)) supports recent calculations of single crystal recoverable strains that show the 20-at.%Hf alloy 

to have ~175 percent of the potential for transformation strain relative to binary NiTi (Ref. 13). It is likely 

that further transformation strain may be achieved through polycrystalline texture optimization not only 

for torsion, but also tension and compression. 

By studying axial and torsional stress—strain curves of Type IV and Type V loading tests on the 

Ni50.3Ti29.7Hf20 alloy (Figs. 14 and 15), it can be observed that plastic strains obtained at the end of both 

tests in the axial and torsional curves differ even though the tests differ only in the sequence of unloading. 

The axial plastic strain is considerably higher in the case of Type IV loading (ATTA) compared to 

Type V loading (ATAT), while the torsional plastic strain is higher in the case of Type V loading 

compared to Type IV loading. This observation explains the need for studying the alloy’s properties in 

different loading paths and supports the recent finding of Richards et al. that the development of plasticity 

is highly path-dependent when the plastic strain is less than or the same order of magnitude as the 

transformation strain (Ref. 14). 

5.0 Conclusions 

There are a number of primary conclusions concerning slightly Ni-rich, precipitation strengthened 

NiTiHf SMA that can be drawn from the results of this empirical study. 

1. Increasing Hf content, even for slightly Ni-rich compositions, result in an increase in transformation 

temperatures (other factors being constant such as Ni content and aging condition). 

2. Increasing Hf content actually results in increasing transformation strains. 

3. The strength of the NiTiHf alloys is considerably higher than the strength of binary NiTi alloys. 

4. The random textured NiTiHf alloy behaves differently in tension, compression, and torsion loading. 

For a random polycrystalline texture, the torsion performance is superior to binary NiTi, but tension 

and compression are inferior. However, new calculations (Ref. 12) have shown that through texture 

optimization, superior performance may be obtained in the other loading modes for NiTiHf alloys. 

5. The development of plastic strain was path dependent for the cases studied in this investigation. 

In addition, the pseudoelastic results obtained in this study for the 20-at.% Hf alloy complement the 

actuation characterization that has been previously performed (Refs. 5, 7, and 9). Combined, these data 

provide a complete actuation plus pseudoelasticity data set on a single high-temperature shape memory 

alloy, which should prove to be instrumental for calibrating SMA constitutive models in future work. 

 
NASA/TM—2013-216619 45 

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